Electrical analogue



Oct. 2, 1951 B. D. LEE 2,569,816

ELECTRICAL ANALOGUE Filed Deo. l, 1947 6 Sheets-Sheet 1 INVENTOR. BURTON D. LEE' A T TOR/VE Y Oct. 2, 1951` B. D. LEE 2,569,816

ELECTRICAL ANALOGUE:

Filed Dec. 1, 1947 e sheets-sheet 2 Moron oM/Trso s55 F/cs. z 5

BURTON D. LEE

BY l' A TTOR/VE Y Oct. 2, 1951 B. D. LEE 2,569,816

' ELECTRICAL ANALOGUE Filed Dec. l. 1947 6 Sheets-Sheet 5 7.76 GAL MNOMETER GAA- VANOME TE R RHEOS TA T /22 TIME SCALE DIAL IN VEN TOR. BUR TON D. L E E BYV l .4 r roRNEY Oct. 2, 1951 B. D. LEE 2,569,816

ELECTRICAL ANALOGUE Filed Dec. l. 1947 G'Sheets-Sheet 4 AMHWEP WEUST I I I I I I I I I I l I I I I I l I TMASCALE HOI( LNVENTOK BUPTQN D LEE www,

Oct. 2, 1951 B. D. LEE

LECTRICAL ANALOGUE: l

6 Sheets-Sheet 5 Filed Deo. l, 1947 INVENTORL BURTON D.

LEE

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Arron/ver F/ELD CO/L K0F MOTOR /60 patented ct. 2, 1.951V

Burto'nD.v Lee, Iousto, Terraassigner` t The `Texas `(vlornpany, New York, Nt Yi, a corporea` tion of Delaware Application Deeemter- "1, 1947, serial No. '788,989`

(o1. zas-6U 4 Claims.

This invention is concerned with the analysis` of mechanical and electrical systems which obey Laplaces equation and provides improvements which greatly facilitate the solution of problems in hydraulics, electrical Iflow in conductors, the distribution of mechanical `stresses in loaded structures, the conduction of heat in solids, and the distribution of flux in magnetic, electrical, and electromagnetic fields. It is directed pariticularly to the solution of problems arising in the design of hydraulic structures such as dams and to the design of electrical apparatus including condensers, insulators, conductive terminals and electrical discharge devices such as vacuum tubes, radiation counters, electrostatic lenses, etc.

There is a precise analogy between electrical and hydraulic systems which will be understood fromthe following:

Ohms law for thev flow of electricity is expressed by the equation 6E I --p 6x (1) where I is the current flowing through the unit of areal of a section whose speciiic resistivity is p, and across which there is a voltage gradient is normal to the area) Darcys law for the ilow of iluids through porous media is where V is the rate of ow of a fluid whose viscosity is Il through a unit area of a section having a permeability lc, and across which there is a pressure gradient (n: is normal to the area).

The two laws are identical when the reciprocal of specific resistivity, is made numerically equal to the ratio of permeability to viscosity, in which case uid flow becomes directly comparable to current How and electrical potential becomes directly comparable to pressure.

Electricity, if it be likened to a moving fluid, is incompressible. Consequently Ohms law (Equation 1) may be combined with the equation of continuity for an uncompressed or incompressible nuid (i. e. one which does not, suier change in volume) The equation canv be expressed asfollows, for the flow of electricity il @61. M and yand 5;-0 (3) where zr; y" and e are the coordinates of a three dimensional space taken at rightangles to "each"` other.V

If Equations l 'and 3 are combined, the result is Laplaces equation viz.

This equ'ationgover'ns the flow of electricity in a homogeneous isotropic `conducting medium, but

pressed.

As disclosed iin co-pending` application Serial No. 674,904,` filed. June 6, 1946,- now abandoned,

by Alexander Wolf and the present applicant, the foregoing analogy has been applied to the solu` electrolyte the shape of which is analogous to that of the petroleum` producing structure under-V going investigation.` Wells in uthe structure are represented by electrodes projecting into the model.` In the case of a gas condensate field being subjected to a cycling operation, some of thel electrodes` may represent injection wells and others "extraction wells. Potentials impressed; across the model are adjusted to simulate" in'je'cl tion and extraction rates at the several wells,` and exploration of the potential-gradients thus Setup 4,

throughout the conductive model permits accuratemappng of the invasion front ofthe 'dry gas being pumpedinto the injection wells to di/si" place Wet gas removed through the extraction wells.

similar analogies may be drawn between une flow of "electricity "and the conduction of Vheat in sona thermal conductors, the eispribuuonoflme chanical stresses in loaded structuresand `the distribution of Aiiux inelectrical,` magnetic "or elec-f tromagnetic fields and the instant invention contemplates the solution of `pr'etienne in a num-151er,

of steady-state dynamic systems. `By way of ex-` 3 ample, eld distribution is an important factor in condensers, insulators and in some types of electrically conductive terminals. Shape of the physical elements involved affects the distribution. In accordance with my invention optimum shapes, spacings etc., may be determined accurately in advance by construction of a conductive model, say one having a pool of electrolyte corresponding in shape to a section of the proposed device, which may be the dielectric element of a proposed condenser. Electrical potentials corresponding in magnitude and location to eld forces acting upon the section are imposed across the pool, and the pool is then explored with an electrode at a plurality of points so as to determine the potentials at these points. These potentials are a guide to the distribution of field forces to be expected in the' proposed condenser;

The process of the invention may also be employed in the determination of optimum sizes and shapes for insulators, conductive terminals and for determining improved shapes and spacings for electrodes etc., in vacuum tubes, radiation counters, etc. It may also be employed to predict accurately the amount and direction of seepage to be expected from dams resting on porous strata etc.

Apparatus such as that described and claimed byl Alexander Wolf in `co-pending application Serial No. 791,797, led December 15, 1947, may be employed. However, operations are facilitated through the use of apparatus of the type described and claimed in the aforementioned copending application Serial No. 674,904, led June 6, 1946, by Wolf and Lee.

The conductor of the model may be of the electronic type, i. e. a conductive solid. Electrons are introduced at one or more points in the model and displace free electrons throughout the conductor, so that electrons are forced to move out at another point, with resultant current flow. As indicated' above, the conductor may also be of the ionic type,v say a pool of electrolyte or an electrolyte dispersed in a body of gel, current flow being dependent upon the mobility of ions through the conductor, but with current flow and potential drop established in the conductor just as in the electronic conductors. In both types of conductors, potentials and potential gradients may be determined by means `of probes in contact with the points in question and connected to a. potential measuring device such as a galvanometer.

A more comprehensive concept of my invention and its application to a variety of problems may be had from the following detailed description, taken in conjunction with the accompanying drawings in which:

Fig. 1 is a perspective view of apparatus being employed to investigate eld distribution in a proposed radiation counter in accordance with lthe invention; Y l

Fig. 2 is the plan of the conductive model being employed in the apparatus of Fig. 1;

Fig. 3 is a perspective view of the probe, marker head, and the mechanical linkage of these two elements in the apparatus of Fig. 1;

Fig. 4 is a diagram 4of the circuit employed in the apparatus of Fig. 1 for manual operation;

Fig. V5 is a diagram of the circuit employed in the circuit of Fig. 1 for automatic operation;

Fig. 6 is a diagram illustratingV a time-scale totaling device incorporated in the apparatus of Fig. 1;

Fig. 7 is a chart of equipotential lines and lines of equal gradient yfor the radial n type radiation 4 counter of Fig. 2 as plotted in accordance with the invention; and

Fig. 8 illustrates the application of the invention to the design of a dam structure.

Referring to Fig. 1, a segment of a proposed iin-type radiation counter is constructed having a conducting pool or basin l2, the geometry of which -corresponds to the geometry of a segment of the counter Aas dened on a corresponding chart I4.

, The model I0 shown in detail in Fig. 2 comprises a cylindrical conductive segment 2| representing the cathode of the counter, a concentrically disposed anode 26 and two radial fins l5, I6 corresponding to two of the six radial ns in the counter, and connected -electrically with the segment I2. The radial iins projectl inwardly from the cathode toward the anode along the vertical insulating walls l1 and I6 which with the cathode and anode dene the basin I2 in which the pool of electrolyte is contained. A model similar to the model I0 is shown in Fig. 7 with the data obtainable by the apparatus of Fig. 1 represented thereon.

By means of a current control unit 22 electric currents are passed through the electrodes 20, 2| and the conducting pool, the magnitude of the potentials bearing a direct relationship to the magnitude of the potentials existing in a radiation counter of this type. A multi-electrode exploring probe 23 is provided with two equipotential probing electrodes 24, 25 and two current W line probing electrodes 26, 21 which make contact with the conducting pool. The two electrodes 24, 25 lie on a line which intersects at a right angle the line joining the two electrodes 26, 2. The exploring probe 23 is rotatably supported at one end of a supporting device 28. A mapping device 36, rotatably supported at the other end of the supporting device, has tracing points 32, 33 by means of which current flow lines or equipotential lines may be indicated on the chart. The tracing points 32, 33 lie in a line perpendicular to the line joining electrodes 24, 25 and parallel to the line passing through electrodes 26, 21.

The supporting device 28 consists of braces l34 which support a beam 36, a sliding table 38 which is mounted on the beam 36 in such fashion that it may be moved along the length of the beam, and a cross member -46 which in turn is mounted on the sliding table 38 at right angles to the beam and is free to slide lengthwise across the sliding table at right angles to the beam. The exploring probe and the mapping device are also connected together by means of a shaft 42 and worm and pinion gears 44 so that rotational movement of the mapping device about its vertical axis corresponds to rotational movement of the exploring probe about its vertical axis. A phase-sensitive reversible induction motor 46 mounted on the sliding table is geared to the shaft 42 by means of a Worm gear 4B to provide means for rotation of the exploring probe and the mapping device under automatic operating conditions. A knob 56 is also provided on the end of the shaft 42 to permit rotation of this shaft when the motor 46 is disengaged and the apparatus is operated manually. A cabinet 52 contains a direction amplifier, a time-scale amplifier, a phasesensitive induction motor (Which operates a calibrated time-scale dial 54), a time-Scale totaling device and a revolution counter, all of which are employed for automatic operation of the instrument. The time-scale dial, located on the front assaggio;

onine: cabinet .152-, ist calitratedimi. time units-.ner rived from the reciprocal ofvthe voltage., drop lacross the currentow line electro.des 26,121;` The,- shaftoi-lthei dial i154 is-i-an'extension of theishaft.` of a rheostat loc-ated insidethe cabinet :52. This rheostat forms part offabalancing. circuit Vso de-` signedthatfor aireasonable range of voltage be-` tween the flow line electrodes .26., ..21` the `movement of i the sliding. arm of: the` rheostatrequired forh achieving balance isvery'nearly `proportional to* theV change in u the reciprocal A. ofA-the--Avoltage i differential between-electrodes0216i-21. iFor-irnan-i ual 'operation -a` galvanometer l 156 -is i connected u across the equipotential probing-electrodes 24;. 25.;

to indicate 'when theseelectrodes# are located at points of-fequale1ectrical potential in "the conducting pool |2 Fig. '3 shows detailed constructionof the eX- ploring lprobe 23,-the suiziporting--device28,` and themapping device-3th `already referredtto in con-inection with Fig. 11. `The exploring probe- .has airotatable vertical s'h-afteftsupportedfrom the cross memberd.- `An exploring Vfoot SI5 #attached i toithe lower-end Aof the shaft fi--cornprisesa block.`

6813i a'material such-as a` phenolicl condensation product, i. i e. i machined Bakelite, in i which `four tungsten yrods which constitute. the probing electrodes 24, @25; 26,` 21) Hare mounted. These electrodes are `disposed at fthe fou-r corners of a rhombus,` the equipotentialelectrodes 2.425 lying on `onediagonaland the @currenttiiow line electrodes26; -21 ly-ingonthel oth-erdiagonal.` The axisJ of 'the current flow `line` electrode` -26 .is .the

same 'es fthe axisof thelvertical shaft 64,. so that upon rotation of-the'exploring probe `Zathgother threelprobing electrodes niovefin-a-` circular path around -the electrode 2t Wires 1! attached .to the tops of tthe :four: probinggelectrodes are; connected respectively :to slip `rings .1.2. .Brushes .1.4 contacting the slip .rings are -iprovided .in forder that:` electrical i connections .may t be made. .to the probingselectrodes.withoutdanger offtanglingand movementthereof. `This portion ofthe shaft 18A isfgrooved to .receive `alug orkey 84 on .the cross member.y `82, thereby preventing rotational movementrof `the cross memberf82 with respect .to the shaft 18. The other end ofthecross `:fnemberr2` supports.. the sharptracing. point 33. `Aspringf;`

heldin place on the shaft 1B by acollar '831s provided. to mantainthenormal positionpf .the tip of thetracing point 33slightly above the surface of the map. Aspring-type push buttonswitch 9i).

positioned on the shaft 'it is providedin order thatthe4 sharp .tip of thetracing pointlmaylbe pushed into the surface of the chart during .operationof the apparatus and at thesarne time makean electrical connection atits contactpoint 9| `for operation of `a. time-scale totaling device,

braces c .3L-shown; insFig. .1. The.` sliding table 31.;A hasta recesse. shaped: to: conform `to the cross esce.-VV tion of the supportfbeam 13a-and is-free itomovelaterally withprespectthereto. The sliding table;m 33T-also has another;'recessshaped yto r conform 1to1. the `cross-fsecti'onof the cross' member 40 andin which that Vcross membery is ffreezto slide laterally ati right:an-glesftoV the support beam 36.

'The shaft .4.2. which connects Vthe exploring; probefandvmapping device by. means ofthe iden4 ticaliworm and pinion gears 44,is rotatablysupr portedbybearings 92ginrbrackets 94, whicharev mounted on the cross membertil. Bygadjustmentf: offthe .Wormand piniongears, the relativeposi-V tionanfd'direction or the transferpoints 332, `33` isirnade to coincide with thatof the current iloveline electrodes orzthe` equipotential electrodes Upon rotation of the shaft 42, either manually' by rneansof the knobr, or automaticallyibymeans of the motor shown in Fig. 1,.thez.ex1.

ploringprobe andthe mapping device rotates'imultaneously, the relative position and direction` off the transfer points with respect to theaelee trodes,y beingidentical forV any angle of rotation.

Fig.` iA shows Vthe electrical circuit for manual Current is supplied oper-ation. of thewapparatus. to-the electrodes Ei-andZl by means of theA current control unit 22. This unit contains avariable-fautotransformer 96 (for supplyinglan .adjust--v ableesource -of voltage).4 an isolation` transformer.

98';areversingswitch 100; electrode circuits: eachv consisting of a rheesta-t` H12 in series with` a'precision xedrresistor |94 and a plug-in xed resistor IDB, the value of which is determinediby.

the conditions of` the problem. By choosing'between sockets lHi8 and H0, into whichlonefenc? ofthe plug-in resistormay be inserted, the di-v rection `of current owing through vany `fixed electrode may be selected. The other end of .the A rectifier type voltmeter H4 is provided for con. nection across .the precision resistor IM of any. electrode circuitby means of aselector switch,

plug-in resistor is inserted in a socket H2.

notshown, in. order that the voltage drop across the'precision fixed resistor may be measured and themagnitude ofthe current iiowing in that cir-` cuit determined. Although only two of the elec-` trodeleadsare required to supply electrodes 201 the embodiment shownl in Fig. 8.

The equipotential probing electrodes'24, 25Yare connectedtto agalvanometer 56, which is of the nullindicatingitype and serves to show whether orfnot the. equipotential electrodes are located at points ofequal potential in the conducting I-pool.

The current flow line electrodes 26, 21-are connected to a time-scale balancing circuit -so that the voltage differential across these-electrodes is-in opposition to a fraction of a-stand ard voltage supplied by an autotransformer llt-anda transformer H8. The input side of` theautotransformer is connected to the output side of the autotransformer 96. whichregulates the'voltage supplyin the current control unit. B'y using the voltage supply for the current control unitasasource of the standard voltage, the" arida yari'ableresistance or rheostat 22, in se` ries with the standard voltage. The fraction off'stanfdard voltage applied across the resistance |-2Uir'i opposition to the voltage across the electod'es 26, 21 is adjusted by means of the rheostat |22, until a galvanometer |24 indicates that the two opposing voltages are in balance. In the balanced position the voltage drop across the resistance |28 is equal to the voltage diierence between the electrodes V26, 2l. The movement of the sliding arm of the rheostat |22 required to obtain this voltage drop across the resistance is approximately proportional to the change in the reciprocal of the voltage diierence between the electrodes 26, 21. The time-scale dial 54 .is attached to the axis of the sliding arm of thevrheostat |22 by a shaft |26, so that the degree'of rotation of the sliding arm, and therefore the amount of resistance placed in the standard voltage circuit by the rheostat |22 is indicated by arbitrary calibrations on the dial. Since the distance between the electrodes 26, 2'| is-very small as compared to the dimensions of the conducting pool l2, the voltage difference between these electrodes may be considered to be a measure of the potential gradient along a current flow line and this potential gradient may bei presumed to be essentially constant at an points between these electrodes. Since potential gradient in the conduction model is anologous to the gradient in the system under examination and since the time required for a unit of Iiuid for example to traverse an incremental length of flow line is proportional to the reciprocal of the pressure gradient'fthe reciprocal of the voltageA difference between the electrodes 26, 21 is proportional to the transit time of an element of iuid along the equivalent incremental length of flow line in the uid flow system of Fig. 8, for example. Ilhe calibrations on the dial 54 therefore represent transit time for the flow of fluid in arbitrary time-scale units which are inversely proportional to the total current supplied to the model and consequently to the total rate of flow of fluid. In the exploration of electrical iields in'accordance with the method of the present invention, the time factor has no signicance but it is, highly desirable to obtain the potential gradients. lIhis may be accomplished by revising the apparatus so that the time-scale dial shows the gradient directly or more simply the time-scale dial may be read and its reciprocal (gradient) obtained mathematically. The position of the current flow line electrodes 26, 2'|

with respect to the conducting pool is recorded on the chart by means of the mapping device and a line connecting the two points indicated .on the chart by the tracing points 32, 33 repre- ;sents the portion of the current ilow line for 'which the transit time is determined by the greading obtained on the time-scale dial.

Fig.V 5 shows an electrical circuit for fully auto- :matic operation of the instrument of Fig. 1 et seq. The circuits for the current control unit 22 :and the time-scale balancing circuit for deter- :mining the potential dierence between the electrodes 26, 2 are the same as described in connection with Fig. 4 for manual operation.

The exploring probe 23 may be made to automatically seek points of equal potential for the probing electrodes 24, 25 by replacing the galvanometer E6 with a direction amplier |28, which detects and amplies any voltage difference existing between these equipotential electrodes. Any amplifier capable of handling a 60 cyclesignal without introduction of` excessive*l harmonic or phase distortion and having suicient power output to operate the motor 46 may -be used. In the particular case illustrated by Fig. 5, the VVdirection ampli-ner consists of asingle voltage 'amplication stage resistance coupled., to a driver stage which in turn is transformerA coupled to a power amplication stage consisting of two GLB tubes in push-pull class B operaplii'ler. In the motor 46 (which is of the shading pole induction type commonly known as a servo-motor) excitation of the main field windings is obtained by a 110 volt, 60 cycle power sup-[ ply and excitation of the two sets of shading coils is obtained by means of the output of theldirection amplier |28. When the shading coils are connected in series the direction of rotation of the motor 46 depends on the relationship of the phase of the currents in the main exciting field and in the shading coils. If a dilerence in potential exists between the equipotential probing electrodes, this potential difference is amplified and applied to the shading coils of the servo-motor. As a result the armature of the motor 46 rotates. This causes rotation of the exploring probe 23 in a direction tending to reduce the difference in potential between the equipotential electrodes. When an equipotential state is reached no signal is applied to the amplifier and no excitation is applied to the shading coils so that no further rotation of the motor takes place. Because of the mechanical linkage between the exploring probe 23 and the mapping device 3c, rotation of the latter is obtained simultaneously so that when a state o1 equal potentials is reached for the equipotential electrodes, the position of the transfer points 32, 33 with respect to the chart corresponds to the position of the flow line electrodes 26, 2 with respect to the model.

Operation of the calibrated time-scale dial 54 may also be carried out automatically by replacing the galvanometer |24 of Fig. 4 by a timescale amplifier |30 and providing time-scale phase-sensitive induction motor |32 to simultaneously operate the sliding-arm of the rheostat |22 and the time-scale dial 54. Any amplier capable of handling a cycle signal without' introduction of excessive harmonic or phase distortion and having sufcient power output to operate the motor |32 may be used. Fundamentally, the construction of the time-scale amplifier is equivalent to that of the direction amplilier |28. The output of the amplier |30 supplies power to the shading pole windings of a timescale motor |32 through an impedance matching transformer contained in the ampliier.

. A shaft |34 connects the sliding arm oi the rheostat |22 Awith the shaft of the motor |32, so that rotation of this motor determines the amount of resistance placed in the balancing circuit by the rheostat. If the fraction of the standard voltage opposing the voltage dilerence across the electrodes 26, 21 is not exactly equal to this voltage difference, this inequality is applied to the amplifier |30 and the amplified signal in turn operates the motor |32 in a direction tending to reduce the inequality in voltages. Thus the sliding arm of the rheostat |22V is moved to a position which will place in the .fthecam |44.

`the shaft of the motor |32) so that the dial,y

rotatessimultaneously and inaccordance With vthe sliding armof the `rheostat |22, therebylindicating in .arbitrary time units the position of that sliding` arm. Y

The process of manually recording and total- -ing all of the time-scale readings observed on the calibrated time-scale dial for the numerous individual operations required for establishing veach-current line charted during the operation ofthe apparatus may be eliminated by employ-` inga time-scale-totaling device |38 and a revolu- `tion counter |40. The former is connectedby ashaft |42 to the .tirne-scale dial 54 and is con- .,trolled by the. position thereof.

'The details-` of the time-scale totaling deviceL :areshown.schematically in Fig. 6. Referring to this figure, a cam |44, mountedon a shaft |42 isffdriven by the time-scale |32, and is so shaped that-,the angle through which a feeler arm |45 qmust :advancefrom its initial Zero position to,A

`touch the camA |44` is directly proportional to the reading-ofthetime-scale dial 54 throughout the @entire scale. Thefeeler arm is provided at` each fendV withinsulated electrical contact pins |43,

.|50 andisA coupledl by a friction drive bearing ,|5 2fto r a shaft |54, which in turn is coupled through a suitable geartrain |55 to a shaft |58,

gandwby means of `a disengaging-type coupling |59 r1to1-.arfreversible induction-- motor |511. Theshaft |58 ofthe-motor |60` is*` also `coupled throughv a suitablegear train 2;=to ashaft llv/hich drives the revolution counter |40 through a ratchet 1.165,; so that the dials of the counter advance on the forward `stroke ofthe `feeler arm toward the-cam, but are undisturbed on the reverse stroke of the 4feelerg-arm to its `original or zero position. 'Ilhe dimensions ,of-'the camand the feeler arm areso chosen that in conjunction with the duction motory Ii; A battery |15 is also provided to supplyfcurrent for actuation of relays |12, |14.

Operation of the totaling device is started by closing Ythe'contacts of the push button 9@ located on the mapping device 39. This completes the energilzoecircuit of a C011 sie of the remy n2,

` thereby closingi contacts |18, |35 whichvare locked intoposition lby a locking key |82.

Theu poxvercircuit `for operation of the motor |69is completed throughthe contact |85. of, the relay |12 and a Contact |34 of the, relay |14. -'Ijlrenthe feeler arm |46` advances untilit touches When Contact ismode with the earn, the circuit `for `ernergizing Athe c oil 86 of the Vnew l ilv .is Completed, cousine Contact 18,410 ,Open andtboootoois lo@ and 1,911 tor close- Vsiparioe. .of the., Contact. les breaks .the power .circuitlfor the forward operatonofthemotor |60 ...andthe .Closure .of `the .contact` |88 ,completes the Power, Ciroutfor reverse ,ooeratiooofthe motor 15051511115 ,online thefselorormitoits original zero positionf-l 01.05.11??.ofthe-@meot |911 insures u,model is all` analogue.

. position., `the counter ratchet |66 slips andthe `dials ofV theV revolution counter |40, areundisturloed. .the nal reading` on thedals .corresponding to the numberof` time-scale unitsiindicated by the time-scale dial5.

`The `.operation ofthe appratusto obtain the information shown in Fig. 7 is asfollovvs:

The. modems constructed to represont..a,.radia1 n type. radiation counter. Thefoutlinevofmthe model corresponds tothe geometryof av60 sector of thecounter. The completed modelis placedkin position `.underthe.exploring probe .andtheleads ,fromy the fixed. electrodeaare connected tojthe current oQ-ntrol unit. Thechartis correspondinely placed `innosition under the mapninedevice. The conductingfpool |2 is filled with a .dilute aqueous solution of an electrolyte Tsuchas Vcopper sulfate or other ionizable salt. The exact concentration .of` saltrin the solution is notollical but theconductivity of the solution ShQuldlbelow in order that .thewpotential drop ybetween thecurrent flow line electrodes 2B, 21` will be of ,an easily measurable.magnitude at. 10W current densities.`

The electric` currentpassingthrough eaohlectrede is. adjusted t in direct, relationship .to .the potentialsin .the radiation, counter, of `which the Adjustment ofthe iodividual t potentials of eacheleQtlode ,is obtained by meansof the Variable resistors llandthexed plug-.in resistors 0,6.

The tracing `points 3233 always. conform in angular position, to theexploring probes`26, ,21. In mapping currentilow lines, which aremnormal to equipotential,1ine s,theprobes 24, 2,5,..areused as equipotentialgprobes.and probes 26, 2.1` (which lie .cna lineperpendicular .to t that `joining probes 2.4, 2,5) `are usedasgradient probes. If. however, it is desiredto .follow an equipotential linerather thana current ovv line, the commutatng (reversing) switch 2|5` is thrown so astoconnect theV probesZ, 2,1 in the equipotential cireuitand theprobes, 2,4, 25 to the gradient circuit. The tracingpointsl, 33,.Will.then bein a position to map points on the equipotential line.

In Adelgermiriing the conditions` prevailingima discharge, device such, as a `radiation Ycounter' or vacuum tube, ,the shapeand location of` equipotentiallines areof importance. In 4.plotting the equipotentiallinesshovvnfinFig. 7, the leads from t. hlfflovv. line probes 2 6 21, are connectedV .to thegalvanorneter 5 6` by means.` of the quadruple p ole double throwswitch 255 (Fig. `4). Theelectrode A25 of the `exploring probe.23` is4 placedrat a portion of a current now line. because the current now line lies perpendicular to the line of equipotential as dened by the two probes 24, 25 and because the tracing points 32, 33 are aligned perpendicular to the probes 24, 25.

point 32 so that the two define a ow line.

il' i tracing points 32, 33, and for this reason, when the galvanoxneter registers Zero, indicating that the probes 26, 21 are at points of equipotential,

the process is repeated until an equipotential line ,i 'is traced out on the chart as far as desired. A permanent record of the equipotential curve is K obtained by drawing a curve through the points of equipotential thus mapped out by the tracing points 32, 33. By repeating the above procedure l. with different starting locations of the probe 26, a series of equipotential lines may be plotted, as shown on Fig. '7.

To determine the potential along any particu- Q lar equipotential line, the galvanometer 266 (Fig. 4) is connected between the slider of the potentiometer 261 and one of the exploring electrodes employed to find the equipotential line, say the electrode 26, the end points of the potentiometer being connected between the field electrodes. In

` this manner the potentials of each of the equipotential lines plotted may be established and Y" recorded as shown in Fig. '1.

To determine and plot the equal gradient 'lines identified in Fig. 7 by the postscript E G., the leads extending from the probes 26, 21 to the Vgalvanometer 56 are interchanged with the leads extending from the probes 24, 25 by means of the quadruple pole switch 265. The tracing points 32, 33 of the mapping device will then denne This is true In manual operation of the instrument for obtaining the current flow lines from which the equal gradient lines are established, the exploring probe is rotated by turning the knob 50 until the galvanometer 56 connected to the exploring v velectrodes 24, 25, indicates that the exploring j electrodes 24, 25 are at pointsl of equipotential,

thus swinging the tracing point 33 around the The chart is then punched or marked by pressing down the tracing points and the gradient for that portion of the current line defined by trac- Ving points 32, 33 is noted. The sliding members of the supporting device 28 are then moved so that the tracing point 32 occupies the former position of the tracing point 33 and the process is repeated until a current line is established on the chart by a series of dots. A series of current lines may be established by repeating the above procedure from different starting points. A` permanent record of each current line may be obtained if desired by drawing a curve through the individual dots in each series mapped out by the tracing points 32, 33. Such a plot is not of particular importance in determination of the conditions prevailing in discharge devices of the type here under consideration.

However, the courses of the current lines areimportant in establishing the equal gradient lines.

'- tween the two.

fwould be identical.

In this respect the type of apparatus which has been developed for reservoir analysis is normally employed to measure potentials along flow lines and to display a number which is proportional Yto reciprocal of the gradient between points along the line. The reciprocal of the gradient thus obtained is representative in fluid iiow studies of the transit time of the fluid flowing in a porous medium. Such use of the apparatus is described in the aforementioned co-pending application. However, in the investigationof electrical conditions within a counter, as above indicated, the interest is centered in the gradient rather than in its reciprocal and it is important for this reason to establish points of equal gradient along the various current lines. It is possible to revise the apparatus of Fig. 4 so that the gradient rather than its reciprocal may be read directly, but rather than make these electrical and mechanical changes, the dial which indicates transit time may be read and its reciprocal obtained mathematically.

In actual practice, in establishing the equal gradient line, the dial which indicates transit time is read periodically as each current line is being plotted and equal gradient lines are established by connecting' points of theoretical equal transit time with a continuous curve. The total transit time at each recorded point on a current line is obtained by adding all increments of transit time (i. e. the transit time for each increment of the current line as defined by the tracing points 32, 33) to that point. This sum is noted on each flow line opposite the corresponding point. To obtain the value of the equal gradient lines thus plotted, the reciprocal of the transit time represented by each of the gradient curves is obtained mathematically from the theoretical transit time represented by that curve.

As indicated above, the equipotential lines and the equal gradient lines are of primary interest when exploring electronic apparatus and the current lines are of secondary interest only in establishing the equal gradient line. However, as shown in Fig. '7, the directions of the current lines are indicated by arrows. The information obtained with the apparatus is a vector quantity, and the direction of the gradient is indicated by the direction of the arrow in each case, and the magnitude of the gradient is shown by each adjacent equal gradient line E. G.

The information plotted on Fig. 7 gives an accurate idea of the eld distribution within one segment of the radial iin type radiation counter. The conditions existing in the other segments Generally speaking, the information plotted on Fig. '7 indicates that a radial n type counter of this particular design is not optimum since the eld is not well distributed throughout the cross section of the apparatus.

Whereas the information superimposed on the model shown in Fig. 7 is identical with that obtainable from the'model shown in Fig. 2, there are certain diiferences in the two models representative of alternative means of construction thereof. Thus in the model illustrated in Fig. '1, the radial fins 202, 203 projecting inwardly from the segment 20| of the cylindrical cathode serve as retaining walls for the solution in the basin 200. In this model the insulating Walls 205, 206 project radially outwardly from the anode 204 to the radial ns 202, 203 forming a continuous surface therewith. The use of this model and the results obtained therefrom are identical to the use of the model shown in Fig. 2.

As already mentioned., various. operations 'can vbe `carried out automatically. For examplatthe rotation vof 'the exploring probe 23 Vcan beV achieved automatically vby means of `the motor it operated by the direction ampli'er |28. Theibalancing of .i

the rheostat `|22 can be performed automatically yby `means of the motor 32 operated by the timescale amplier |30. 'By means of the time-scale totaling device |38 and the lrevolution:counter Mil, .gradients or time-scale units, being thereciprocal ofthe gradient, for any speciiied interval ialong a current flow line may be Vcomputed auto- :maticallyas the current dow line is traced.

i In automatic operation for the determination of current flow lines for example the exploring i probewill rotate tol obtain a position such that no potential difference exists betweenthe equi- -i `potential electrodes 24, 25. As long as any difference in potential exists between these electrodes,

Y lit is Iapplied to the `direc-tion amplifier |28 and ther` amplified voltage is 'applied to the `s'lradlng coils of the. motor 4t to cause `rotation of the motor in a `direction such that the exploring ,probe .is

turned to a position where no differencein potenl -tial `occurs between the equipo'tential probes.

During the time the vexploring foot "oriprobe is thus oriented, the time-scale balancing circuit is also seeking a balance through the adjustment of `the rheostat |22y and the rheostatwill` `come to rrest shortly after the direction system. has

l .reached a balance. Thisuis achieved through the `potential balancing icircuitfand the time-scale amplifier |30 andthe motor |532. As long as the frac-tion of the standard voltage supplied from kthe 4transformer i itin opposition-to the `poten- `.the flow line electrodes 26, 2l.

With both direction and time systems at balance the instrument indicates'both the direction foi the 'current dow line by the angular position of theveXplor-ing foot and' the `gradient or equivalent transit time across that section -of .flow line i by the reading of the calibrated timesscale dial 54. This information maybe recorded :by @pressing the'push button Se on the mappingrdevice 3G. This simultaneously depresse's the tra-cingupoint 33kt@ make a punch mark on the chart and'also closes the electrical contacts 9|, `which causethe timeescale totaling 4device les to `register on .the @counter Mt.

`Various desi-gnsiare possible for the potential i balancing circuit and the direction `and timescale ampliers as well as in the probe and 'the other elements of the apparatus. Likewise, the specic design of the time-scale totaling device is not a limitation of the invention and any equivalent mechanism may be employed. Because of the wide variations in vpotential gradient which can occur over the surface of the conducting pool it is sometimes desirable to provide two or even more time unit scales to achieve greater accuracy in determining these gradients.

In exploration of other types of electrical equipment by the method herein set forth, a model of the field under consideration is substituted for the model of the radiation counter denser, is employed.

`herein described. For example in the. examinati-on of the eld characteristics in the dielectric of a condenser,` a model conforming `in planfto. a vertical section of the condenser and havingitwo electrodes representing the plates of the con- Alternatively the eld forces developed in a vacuum tube, sayv a triode,

`may be ascertained using a circular pool of electrolyte with electrodes therein to representthe lament, grid and plate. It is apparent that' by l the construction of a proper model the iield char- Improved results are obtained by constructing a model in which the proposed dam cross-section is represented by a-blcck of insulating material and the porous rock by a pool of electrolyte. Thus; as shownin Fig. 8, a basin 250 of insulating material with vertical side Walls 25|,` 252i, 253, 254, 255 is closed by another insulating mem-ber 259 corresponding `in shape `to the cross-section of the proposed dam. A' plurality of injection electrodes 256 are disposed in the side 275| of the basin (which is shaped to 'correspond' to the upstream surface of the rock) and-a plurality of extraction electrodes 251' areHd-isposed inotherside 255 of the basin (which corresponds to theidownstream surface of `the rock). Iny other 4word-s the basin and the dam `model, as viewed in plan, :simulate a vertical cross-section through `the dam and the underlying` formation, taken along the line of water flow.

The basin is iilled with electrolyte and the inf jection and extraction electrodesare connected toa current control unit, such as that shown in Fig. `4 or 5 and the potentials are adjusted to simulate hydraulic conditions in the rock forma' tion to which `the electrolyte corresponds.

VCurrentA ow lines and `eduipotential lines are then investigated and plotted as already described.

ap'entode for example, or the dam representedin .8, aigreaternumber of circuits are required.' In this application of the invention, the vcali-- brated time-scale, i. e. the reciprocal of the potential gradient, is employed to ascertain the rate of liquid flow. Thus it is possible to ascer-i tain in advance not only the path but also the rate of seepage for any given construction.

By varying the distance 258 that the dam 259 projects into the rock formations or basin and by changing the shape of the "dam, at its contact with the formation and by making electrolytic model studies in each case, the optimum design of a dam may be determined.

I claim:

1. In determining iield distribution in an electrical device, the improvement which comprises imposing on a pool of electrolyte corresponding in shape to a section of the device electrical potentials corresponding in magnitude and location to field forces acting upon the section, ex-

ploring the pool by moving at least one electrode therein in a direction corresponding to that extending across the section to locate a line of f lequipotential points in the pool, moving the electrode similarly in the pool to locate another line of equipotential points diiering from the potential of the rst line, plotting current flow lines normal to the equipotential lines thus located on a chart of the section, locating points of equal electrical gradient on the flow lines in the pool lthus located by electrical measurement of the gradient along the linesy and plotting the points of equal gradient thus located on the chart.

' 2. In determining field distribution in an electrical device, the improvement which comprises imposing on a pool of electrolyte corresponding in shape to a section of the device electrical potentials corresponding in magnitude and location to eld forces acting upon the section, locating two points on a rst equipotential line in the pool extending in a direction corresponding to that across the section, simultaneously locating on a chart of the section two spaced points defining a flow line corresponding to a portion of a current flow line perpendicular to the rst equipotential line in the pool defined by the two points thereon, thereafter locating two points on a second equipotential line in the pool extending in a direction corresponding to that across the section but spaced from the rst equipotential line and passing through a point corresponding in location in the pool to the location of one of the two spaced points previously located on the chart,

`simultaneously locating on the chart an extenline in the pool, measuring the potential gradients between the points in the pool corresponding to the spaced points on the chart, and locating points of equal potential gradient on the chart.

3. In determining liquid flow through a porous body, the improvement which comprises imposing onY a pool of electrolyte corresponding in shape to a section of the body electrical potentials corresponding in magnitude and location to theV hydraulic forces tending to cause liquid flow through the section, locating two first points on a first equipotential line in the pool and eX- tending in a direction corresponding' to that across the section, simultaneously locating on a chart corresponding to the section a portion of a ow line deiined by two spaced points perpendic- `ular to the equivalent position of the two first points in the pool, thereafter locating two points on a second equipotential line in the pool oilset from the rst equipotential line and passing through a point in the pool corresponding in position to that of one of the spaced points on the chart, simultaneously locating on the chart a continuation of the flow line perpendicular to a line through the equivalent positions on the chart of the points onv the second equipotential line in the pool and defined by said one of the spaced points on the chart and a third spaced point on the chart, measuring the potential gradients between the points in the pool corresponding to the spaced points on the chart, and locating points of equal potential gradient on the chart.

4. In apparatus for plotting eld distribution, the combination which comprises a potentiometric model including a pool of electrolyte corresponding in shape to a system in which the eld is distributed and means for imposing on the pool electrical potentials corresponding in magnitude and location to forces acting upon the system, a probe head mounted adjacent the pool and carrying at least three probes in contact with the pool, one set of two of the probes defining a line transverse to a line drawn through a different set of two of the probes, a chart, a marker head disposed adjacent the chart, means for laterally moving the probe head and the marker head in unison, means for rotating the probe head and the marker head in unison, two markers on the marker head corresponding in orientation to two of the probes on the probe head, potential measuring means, and switching means for connecting the potential measuring means to either of the probe sets.

BURTON D. LEE.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STA'IVES PATENTS Number Name Date 1,918,001 Stone July 11, 1933 2,423,754 Bruce July 8, 1947 OTHER REFERENCES Some Applications of Field Plotting, by E. O. Willoughby; I. E. E. Journal, vol. 93, part 3, July 1946, pp. 287-291.

Conformal Transformation with the Aid of an Electrical Tank, by Bradeld, Hooker and Southwell; Proceedings of the Royal Society of London, vol. 159-A, April 1, 1937, pp. 315-346.

Automatic Plotting of Electrostatic Fields,

by Paul E. Green, Jr., Review of Scientific In- 

